FALL RIVER — Someone is out to destroy the vacant multifamily house at 1945 Bay St., which was intentionally set on fire Tuesday night for the third time since Christmas.

“That house needed to come down. I predicted this would happen, and it did,” said a frustrated Fall River fire Capt. Neil Furtado, who responded to the fire just after 10 p.m.

Just like the last blaze on May 30, arsonists set fire in the abandoned home’s basement. This time, the flames caused even more substantial structural damage, with the roof and second floors collapsing inward into the basement, Furtado said.

No firefighters were injured, and the fire did not spread to other nearby dwellings. But arson fires present serious public safety concerns. Local officials have had plenty to worry about lately — the Bay Street blaze was the fourth arson in Fall River within the past two weeks.

Earlier on Tuesday, just before 8:15 a.m., someone broke into a seafood van near the corner of Dyer Street and President Avenue and stole a cash register. They then set a chair on fire inside the van, using a can of spray paint as an accelerant. The fire caused about $2,500 in damage, officials said.

Last weekend, several young people were said to have lit trash barrels on fire outside the Urban Elements Hair Salon, 34 Old Borden St. The heat cracked the salon’s window, but firefighters prevented any further damage.

On June 29, someone set a car on fire in the driveway of a Hyacinth Street residence. The flames destroyed a camper, damaged a swimming pool filter and melted some of the home’s vinyl siding. The residents woke up just after the fire started at 3 a.m., ran outside the house and called 911. Investigators later found a burned rag that had been inserted into the car’s fuel tank and lit.

Police and fire investigators have not publicly identified suspects in any of the recent arsons. Mayor Will Flanagan urged residents to report any suspicious activity to police.

“Fire is not something to play with, and its results can be devastating,” Flanagan said. “I have full confidence in our fire investigators that they will fully investigate these arsons and then hold the individuals responsible for them.”

When asked whether the recent layoffs of 26 firefighters makes the city more vulnerable to arson fires, Flanagan said: “Cities are often called upon to do more with less, and we will respond to and continue to protect and serve the community as we did (Tuesday) night.

The number of structure arsons fluctuates every year in Fall River. Last year, firefighters responded to at least 14 structure fires that were later determined to have been intentionally set. In 2011, there were four such arsons in Fall River, but there were 17 structure arsons in 2010 and 16 in 2009, according to the Massachusetts Fire Incident Reporting System.

“It’s unfortunate that we have arsonists in the city who do these types of things. They have no regard for the surrounding houses or families, or firefighters or police officers that have to respond,” Fall River City Buildings Inspector Joseph Biszko said.

“If someone is seriously injured in this or killed, then hopefully we’ll get them, and they’ll spend some jail time, maybe the rest of their lives, thinking about what they’ve done,” said Biszko, who added that he is finishing the paperwork to award a contract to AA Wrecking to demolish the Bay Street house.

“We’re trying to expedite this,” Biszko said.

On May 30, when the Bay Street house was last targeted by arsonists, Furtado said the structure’s integrity had been weakened to the point that it needed to be demolished. Furtado said Wednesday that he had reiterated his concerns to city officials.

“It’s an embarrassment, in my opinion. That house needed to come down now,” Furtado said.

Firefighters from two ladder trucks and four engine trucks responded to Tuesday night’s fire. At one point, thunderstorms prompted firefighters to halt ladder operations and use handlines instead to finish off the fire, Furtado said. Witnesses did not report seeing any suspects in the area.

The two and a half story, 104-year-old Bay Street house was first targeted last Christmas. In that incident, the arsonists broke into the house, which had already been vacant for several months, and set fire inside the main entrance, near a stairway, just before 1 a.m. That fire gutted the home’s first and second floors, authorities said.

On May 30, just before 2 a.m., a witness reported seeing smoke, flames and a group of young people running from the back of the house. The arsonists lit several “odds and ends” in the basement.

Neighbors who live near the abandoned Bay Street property have expressed their concerns to firefighters.

“They don’t even want to go to sleep at night because they are afraid it’s going to be their house next, or that the fire is going to spread,” Furtado said.

On Tuesday night, firefighters worked to protect a house directly north of the abandoned Bay Street property. Hot, heavy embers were landing on that home’s roof and siding, but firefighters prevented the house from catching fire.

Meanwhile, another abandoned property near the torched Bay Street house is causing additional concern for fire officials. While Tuesday’s fire scene was active, Furtado and other investigators went to that structure to determine whether it was secure.

“And guess what? The front door was busted open,” Furtado said. “There was evidence of a lot of activity there, drug use, people using toilets, all kinds of matches and solvents. This is just craziness.”